English

Pointwise convergence along a tangential curve for the fractional Schr\"odinger equation

Analysis of PDEs 2020-06-08 v1 Classical Analysis and ODEs

Abstract

In this paper we study the pointwise convergence problem along a tangential curve for the fractional Schr\"odinger equations in one spatial dimension and estimate the capacitary dimension of the divergence set. We extend a prior paper by Lee and the first author for the classical Schr\"odinger equation, which in itself contains a result due to Lee, Vargas and the first author, to the fractional Schr\"odinger equation. The proof is based on a decomposition argument without time localization, which has recently been introduced by the second author.

Keywords

Cite

@article{arxiv.2006.03272,
  title  = {Pointwise convergence along a tangential curve for the fractional Schr\"odinger equation},
  author = {Chu-hee Cho and Shobu Shiraki},
  journal= {arXiv preprint arXiv:2006.03272},
  year   = {2020}
}

Comments

14 pages, 1 figure